Question

In figure, $$line\ XY\ ||\ line \ PQ$$ and we have $$\angle ALY=(2x-15)^o, \angle LMQ=(x+40)^o$$, find x.

Answer 1

We have $$\angle ALY=(2x-15)^0$$ and $$\angle LMQ=(x+40)^0$$

Also, $$line\ XY\ ||\ line \ PQ$$

$$\therefore$$ $$\angle XLM$$ and $$\angle LMQ$$ are corresponding angles.

and corresponding angles on parallel lines are congruent.

$$\therefore \angle ALY=\angle LMQ$$

$$\therefore 2x-15=x+40\\$$

$$\Rightarrow 2x-x=40+15\\$$

$$\therefore x=55^0$$